Motivated by the Maximum Theorem for convex functions (in setting of linear spaces) and subadditive Abelian semigroups), we establish a class generalized functions, i.e., $f:X\to\R$ that satisfy inequality $f(x\circ y)\leq pf(x)+qf(y)$, where $\circ$ is binary operation on $X$ $p,q$ are positive constants. As an application, also obtain extension Karush--Kuhn--Tucker theorem this functions.

let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...

In this paper, we consider a vector optimization problem involving locally Lipschitz generalized approximately convex functions and provide several concepts of approximate efficient solutions. We formulate variational inequalities Minty Stampacchia type under the framework Clarke subdifferentials use these as tool to characterize an solution problem.